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Geometry in Design Basics

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Geometry in Design Basics

A community group is creating a small outdoor sign. Use geometry to check the design, calculate measurements and explain how shapes work together. Show working where needed. Use a ruler and protractor if available.

Shape language

Identify and use geometric properties to communicate design decisions.

1.The sign has a rectangular base measuring 1.2 m by 0.8 m. Which statement correctly describes the base?

It has four equal sides and four right angles.
It has opposite sides equal and four right angles.
It has one pair of parallel sides and no right angles.
It has four sides of different lengths.

2.A circular emblem is drawn on the sign. Match each circle term to its definition.

Radius
Diameter
Chord

A segment through the centre joining two points on the circumference
A segment joining any two points on the circumference
A segment from the centre to a point on the circumference

3.The emblem has a radius of 18 cm. Use the number line to place and label its radius and diameter lengths, then state the diameter.

Angles and structure

Use angle facts and properties of shapes to test whether a design will work.

4.A triangular brace has angles of 48° and 67°. Find the third interior angle. Show the angle total you use.

5.The sign frame is a quadrilateral with angles 90°, 90°, 105° and x°. Calculate x and name the angle sum of a quadrilateral.

6.A designer adds a diagonal brace across a rectangular panel. Explain why the diagonal can make the frame more rigid, using the shapes it creates.

7.The sign’s rectangular face is 1.2 m long and 0.8 m wide. Calculate its perimeter and area, including suitable units.

Plan a geometric emblem

Apply circle and polygon properties to make a clear, measurable design.

8.A regular hexagonal motif is repeated around a central point. What is each exterior angle of a regular hexagon? Explain how you found it.

9.For a circular border with radius 18 cm, calculate the circumference using C = 2πr. Give your answer to the nearest centimetre.

10.Sketch a simple sign emblem using at least two different geometric shapes. Label one angle or side length and write one sentence explaining how the shapes support the design. Your sketch should be your own.